A generalization of surfaces family with common spatial geodesic

• Published in: Applied mathematics and computation Vol. 201; no. 1; pp. 781 - 789
• Main Authors: Kasap, Emin, Akyildiz, F. Talay, Orbay, Keziban
• Format: Journal Article
• Language: English
• Published: New York, NY Elsevier Inc 15.07.2008; Elsevier
• Subjects: Common geodesic; Differential geometry; Exact sciences and technology; Functions of a complex variable; Geometry; Global analysis, analysis on manifolds; Marching-scale functions; Mathematical analysis; Mathematics; Numerical analysis; Numerical analysis. Scientific computation; Ruled surface; Sciences and techniques of general use; Surface family; Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds; Surface family; Common geodesic; Ruled surface; Marching-scale functions; Numerical analysis; Sufficient condition; Applied mathematics; Decomposition method; Geodesic; Surface
• ISSN: 0096-3003; 1873-5649
• DOI: 10.1016/j.amc.2008.01.016

We analyzed the problem of constructing a surfaces family from a given spatial geodesic curve as in the work of Wang et al. [G.-J. Wang, K. Tang, C.-L. Tai, Parametric representation of a surface pencil with a common spatial geodesic, Comp. Aided Des. 36 (5) (2004) 447–459], who derived the sufficient condition on the marching-scale functions for which the curve C is an isogeodesic curve on a given surface. They assumed that these functions have a factor decomposition. In this work, we generalized their assumption to more general marching-scale functions and derived the sufficient conditions on them for which the curve C is an isogeodesic curve on a given surface. Finally using generalized marching-scale functions, we demonstrated some surfaces about subject.